3x-3c=2x+5, where C is integer show that x cannot be a multiple of 6

Answer 1

3x-3c=2x+5 => x = 3c + 5.

If c is an even integer, then x = 3c + 5 is odd and cannot be a multiple of 6 (which would be even).

if c = 2k+1 for some integer k, then x = 6k + 3 + 5 = 8 which cannot be divisible by 6.